Standard +0.3 This is a standard Spearman's rank correlation test requiring ranking data, applying the formula (possibly with tied ranks), and comparing to critical values. While it involves multiple steps, it's a routine application of a learned procedure with no conceptual challenges beyond remembering the method—slightly easier than average since it's purely procedural.
A researcher claims that, at a river bend, the water gradually gets deeper as the distance from the inner bank increases. He measures the distance from the inner bank, \(b \mathrm {~cm}\), and the depth of a river, \(s \mathrm {~cm}\), at seven positions. The results are shown in the table below.
Position
\(A\)
\(B\)
\(C\)
\(D\)
\(E\)
\(F\)
\(G\)
Distance from
inner bank \(b \mathrm {~cm}\)
100
200
300
400
500
600
700
Depth
\(s \mathrm {~cm}\)
60
75
85
76
110
120
104
Calculate Spearman's rank correlation coefficient between \(b\) and \(s\).
Stating your hypotheses clearly, test whether or not the data provides support for the researcher's claim. Use a \(1 \%\) level of significance.
\begin{enumerate}
\item A researcher claims that, at a river bend, the water gradually gets deeper as the distance from the inner bank increases. He measures the distance from the inner bank, $b \mathrm {~cm}$, and the depth of a river, $s \mathrm {~cm}$, at seven positions. The results are shown in the table below.
\end{enumerate}
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | c | }
\hline
Position & $A$ & $B$ & $C$ & $D$ & $E$ & $F$ & $G$ \\
\hline
\begin{tabular}{ c }
Distance from \\
inner bank $b \mathrm {~cm}$ \\
\end{tabular} & 100 & 200 & 300 & 400 & 500 & 600 & 700 \\
\hline
\begin{tabular}{ c }
Depth \\
$s \mathrm {~cm}$ \\
\end{tabular} & 60 & 75 & 85 & 76 & 110 & 120 & 104 \\
\hline
\end{tabular}
\end{center}
(a) Calculate Spearman's rank correlation coefficient between $b$ and $s$.\\
(b) Stating your hypotheses clearly, test whether or not the data provides support for the researcher's claim. Use a $1 \%$ level of significance.
\hfill \mbox{\textit{Edexcel S3 2010 Q4 [10]}}